What is the derivative of (1+cos(x)sin(x)) ?

The derivative of (1+cos(x)sin(x)) is -sin^2(x)+cos(x)(1+cos(x))

What is the first derivative of (1+cos(x)sin(x)) ?

The first derivative of (1+cos(x)sin(x)) is -sin^2(x)+cos(x)(1+cos(x))

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\frac{d}{d x} ((1 + cos (x)) sin (x))

- sin^{2} (x) + cos (x) (1 + cos (x))

Solution steps

\frac{d}{d x} ((1 + cos (x)) sin (x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 1 + cos (x), g = sin (x)

= \frac{d}{d x} (1 + cos (x)) sin (x) + \frac{d}{d x} (sin (x)) (1 + cos (x))

\frac{d}{d x} (1 + cos (x)) = - sin (x)

\frac{d}{d x} (sin (x)) = cos (x)

= (- sin (x)) sin (x) + cos (x) (1 + cos (x))

Simplify

(- sin (x)) sin (x) + cos (x) (1 + cos (x)) : - sin^{2} (x) + cos (x) (1 + cos (x))

= - sin^{2} (x) + cos (x) (1 + cos (x))

\frac{4}{( s + 2 ) ^{3}}

x \to 0 lim ((3 x + 1))

f (x) = lo g_{10} (x)

\int \frac{x ^{2} + 2 x + 4}{( x + 1 ) ^{3}} d x

What is the derivative of (1+cos(x)sin(x)) ?
The derivative of (1+cos(x)sin(x)) is -sin^2(x)+cos(x)(1+cos(x))
What is the first derivative of (1+cos(x)sin(x)) ?
The first derivative of (1+cos(x)sin(x)) is -sin^2(x)+cos(x)(1+cos(x))